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Ebook Optimal control models in finance: Part 2

(BQ) Part 2 book "Optimal control models in finance" has contents: An optimal corporate financing model, further computational experiments and results, conclusion. | Chapter 4 AN OPTIMAL CORPORATE FINANCING MODEL 1. Introduction In this chapter, an optimal corporate financing model (Davis and Elzinga [22, 1970]) has been used since it is one of the well known and pioneering models on optimal control in finance. Some other recent work in this area include [21, 1998] and [61, 2001]. The approaches that were constructed in Chapter 2 and Chapter 3 for the optimal control problems are applied. The model discusses investment allocation in order to decide what proportion of its earnings should be retained for internal investment and what proportion should be distributed for shareholders and dividends in a public utility. The aim is to choose the “smart” investment program that the owners can get most benefits from. In the real world, these kinds of problems are common. Section 4.2 defines the problem of this financial model. Then the analytical solution, which was created by Davis and Elzinga, is discussed in Section 4.3. In Section 4.4, an important technique called “penalty term” is introduced for solving optimal control problems with constraints and end-term condition. By using the “penalty term”, all the constraints become easy to be included into the cost function. The transformations of this model are described next in Section 4.5 for the computation. The computational algorithms for this model are constructed in Section 4.6. A computer software package for the algorithms is shown in Appendix A.3. The analysis and discussion of the computing results are presented in Section 4.7. 2. Problem Description A firm decides how it should generate its finance to maximize the value of the firm, the stock value, or to achieve any other specified objectives. Two well known papers by Modigliani and Miller [59, 1958] [60, 1963] were instru- 92 OPTIMAL CONTROL MODELS IN FINANCE mental in developing the literature on the modern theory of optimal corporate finance. According to this theory, the optimal financial structure of the firm .